US2022364953A1PendingUtilityA1
Compilation Method for Reliability Test Load Spectrum of High-Speed Bearing of Electric Drive System
Assignee: UNIV OF SHANGHAI FOR SCIENCE AND TECHNOLOGYPriority: Aug 7, 2020Filed: Aug 3, 2021Published: Nov 17, 2022
Est. expiryAug 7, 2040(~14 yrs left)· nominal 20-yr term from priority
G01M 17/007G06F 30/17G06F 30/20G06F 2119/02G01M 13/04
43
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Claims
Abstract
The present invention discloses a compilation method for a reliability test load spectrum of a high-speed bearing of an electric drive system. The method comprises the following steps: based on load data of a whole life cycle of an electric drive system, correlating a leading failure load of a high-speed bearing; counting an action frequency of each load level by a multi-dimensional load joint counting method; constructing a bearing mechanical balance equation; determining a reliability test load level by damage contribution distribution and cumulative damage contribution distribution of different load levels; according to a principle of a consistent overall frequency and consistent damage, determining a time of the reliability test load level; and in combination with extreme load working conditions, finally constructing a reliability test load spectrum of the high-speed bearing. The constructed reliability test load spectrum is correlated to an actual failure mode, which can effectively verify a reliability level of the high-speed bearing, shorten reliability test time and provide support for high-quality development of the high-speed bearing.
Claims
exact text as granted — not AI-modified1 - 10 . (canceled)
11 . A compilation method for a reliability test load spectrum of a high-speed bearing of an electric drive system, characterized by comprising the following steps:
step 1 : according to a load spectrum of a whole life cycle of an electric drive system, correlating leading failure loads of a high-speed bearing, and analyzing joint distribution characteristics of multi-dimensional loads of a rotation speed and a torque; step 2 : constructing a high-speed bearing balance equation under the joint loads; the step 2 of constructing the high-speed bearing balance equation comprises calculating different contact loads of the high-speed bearings by a Newton-Raphson iterative method, comprising the following sub-steps: step 2 - 1 : constructing the balance equation of the high-speed bearing under a radial load; and step 2 - 2 : constructing the balance equation of the high-speed bearing under the radial load and an axial load. step 3 : calculating a high-speed bearing life and bearing damage and conducting damage analysis; step 4 : determining a reliability test load level and a time proportion relation of each typical load level; in step 4 , the reliability test load grade is determined according to the following characteristics: characteristic 4.1: different distribution characteristics of damage contribution of the high-speed bearing are involved; characteristic 4.2: selection of the reliability test load grade should comprise the typical working conditions of the load spectrum of the electric drive system in the whole life cycle, and at the same time, the damage contribution should be high; and characteristic 4.3: the reliability test load spectrum comprises extreme load working conditions. step 5 : determining a damage target of the whole life cycle of the bearing; and step 6 : compiling a reliability test load spectrum of the high-speed bearing.
12 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
in the step 1 , a main method of analyzing joint distribution characteristics of multi-dimensional loads for the high-speed bearing is: a multi-dimensional load joint counting method is used to count action frequencies under different rotation speeds and different torque levels in the load spectrum of the electric drive system in the whole life cycle, and the number of turns of the high-speed bearing under the different load levels is obtained.
13 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
a specific method of constructing the balance equation of the high-speed bearing under the radial load comprises: under high-speed bearing centrifugal force, Q i is a contact load between a steel ball and a bearing inner ring, Q e is the contact load between the steel ball and a bearing outer ring, so that centrifugal force F c of a bearing ball is:
Q ej −Q ij =Fe (1)
where j is the number of the bearing ball;
F e =½ mD m ω m 2 (2)
in equation (2), m is the mass of the steel ball; D m is an average diameter of the high-speed bearing; ω m is a revolution angular velocity of the bearing ball; a radial displacement δ 104 of the bearing under the radial load at any angular position ψ j is:
δ
φ
=
δ
r
cos
ψ
j
-
1
2
P
d
=
δ
max
[
1
-
1
2
ε
(
1
-
cos
ψ
j
)
]
,
(
3
)
in Equation (3), δ r is a relative radial displacement between inner and outer rolling paths of the high-speed bearing; P d is a radial internal clearance of the high-speed bearing; δ max is a total elastic deformation at the contact position between a rolling body and the inner and outer rings of a radial load action line;
and ε is a load distribution parameter of the high-speed bearing, wherein ε is calculated as follows:
ε
=
1
2
(
1
-
P
d
2
δ
r
)
,
(
4
)
a contact load Q ij of the inner ring of the high-speed bearing is:
Q
ij
=
Q
max
[
1
-
1
2
ε
(
1
-
cos
ψ
j
)
]
,
(
5
)
Q
max
=
K
n
(
δ
r
-
1
2
P
d
)
1.5
,
(
6
)
where: Q max is a maximum contact load between a roller of the high-speed bearing and the rolling path; K n is a contact stiffness coefficient between the roller and the rolling path of the high-speed bearing;
a radial contact load Qrj of the high-speed bearing is:
Q rj =Q iψ cos ψ j (7)
in equation (7), Q iψ is a contact load at different position angles 104 j ;
according to the mechanical balance equation of the bearing, the radial contact load of the high-speed bearing is obtained; and the mechanical balance equation of the high-speed bearing is:
F
r
=
∑
ψ
=
0
±
ψ
i
Q
i
ψ
cos
ψ
j
,
(
8
)
in equation (8), K n is a contact stiffness coefficient between the roller and the rolling path of the high-speed bearing.
14 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 3 , characterized in that:
when the high-speed bearing bears both the radial load and the axial load at the same time, the inner and outer rings of the high-speed bearing generate relative displacements, comprising the axial displacement δ a and the radial displacement δ r ; the outer ring of the high-speed bearing is fixed; and after the high-speed bearing is loaded, the inner ring of the high-speed bearing generates a relative displacement relative to the outer ring of the high-speed bearing; D b is the diameter of the high-speed bearing ball; D m is the average bearing diameter of the high-speed bearing, and a o is an initial contact angle between the high-speed bearing ball and the rolling path; after the high-speed bearing is loaded, a circumferential radius R i where a curvature center of an inner ring rolling path groove is located is:
R i =0.5 D m +( r i −0.5 D b )cos α 0 (9)
a circumferential radius R o where the curvature center of a rolling path groove of the high-speed bearing outer ring is located is:
R o =0.5 D m −( r e −0.5 D b )cos α 0 (10),
at any angular position ψ, a distance r between the curvature centers of inner and outer rolling path grooves of the high-speed bearing is:
r =[( GD b sinα o +δ a ) 2 +( GD b cosα o ,+δ r ,cosψ) 2 ] 1/2 (11),
in equation (11), r is a curvature radius of the rolling path groove of the inner and outer rings of the high-speed bearing; G=f e +f i −1 , f n is a curvature radius coefficient of the rolling path groove of a high-speed bearing cover; f n =r n /D b , wherein n=i and e, which respectively represent the inner ring and outer ring of the high-speed bearing; δ a and δ r represent the relative axial displacement and the relative radial displacement of the inner and outer rings of the high-speed bearing respectively; dimensionless quantities are introduced:
δ
a
_
=
δ
a
GD
b
,
(
12
)
δ
r
_
=
δ
r
GD
b
,
(
13
)
the following equations are set:
N =sinα o + δ a (14),
L =cosα o + δ r cosψ (15),
in equations (14) and (15), N and L are dimensionless quantities; and equations (14) and (15) are substituted into equation (11), so that:
r=GD b ( N 2 +L 2 ) 1/2 (16),
a total deformation δ ψ , obtained by the contact between the bearing ball and the inner and outer rings of the high-speed bearing at the angular position ψ is:
δ ψ =GD b [( N 2 +L 2 ) 1/2 −1] (17),
according to equation (1), the contact load Q ψ of the inner ring of the high-speed bearing is:
Q
ψ
(
GD
b
K
p
)
3
/
2
[
(
N
2
+
L
2
)
1
/
2
-
1
]
3
/
2
,
(
18
)
in equation (18), K p is an elastic deformation constant ofhigh-speed bearing point contact;
the contact angle α ψ between the bearing ball and the high-speed bearing ring at any angular position is
sin
α
ψ
=
N
(
N
2
+
L
2
)
1
/
2
,
(
19
)
according to balance conditions, the radial load and the axial load acting on the high-speed bearing are F r and F a respectively, so that:
F
r
=
∑
ψ
=
0
±
π
Q
ψ
cos
ψcos
α
ψ
,
(
20
)
F
a
=
∑
ψ
=
0
±
π
Q
ψ
sin
α
ψ
,
(
21
)
equations (20) and (21) are nonlinear equation systems of unknown numbers δ a and δ r ; a Newton-Raphson iterative method is used in MATLAB for programming; small initial values δ a and δ r are set, and parameters of the high-speed bearing are input to obtain the actual deformations δ a and δ r of the inner and outer rings of the high-speed bearing; and equations (14) to (18) are combined to obtain the contact load of the high-speed bearing.
15 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
in step 3 , that method for calculating the life of the high-speed bearing is as follow: based on standards improved by a Lundberg-Palmgren bearing life theory, the life of the high-speed bearing under different load levels is calculated; a calculation method of high-speed bearing damage is as follows: a Palmgren-Miner linear cumulative damage rule is adopted, and a life of the rolling path of the high-speed bearing is L 1 under the working condition of an equivalent dynamic load P I , and if the bearing runs for N 1 turns under the working condition, equivalent damage of the high-speed bearing under the working condition P 1 is: D 1 =N 1 /L 1 ; if the high-speed bearing experiences a random road load and runs for N 1 ,N 2 , . . . ,N n turns under equivalent loads of P 1 , P 2 , . . . P n , the damage caused by the random road load to the high-speed bearing is as follows:
D
=
∑
i
=
1
n
D
i
=
∑
i
=
1
n
N
i
L
i
,
(
22
)
in equation (22), n is a set of working conditions of the high-speed bearing, and for each corresponding working condition i, the fatigue life of the high-speed bearing is L i turns, and under the working condition, the high-speed bearing runs for N i turns, wherein N i <L i .
16 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
the extreme load working conditions comprise the extreme speed and the maximum torque of the high-speed bearing motor of the electric drive system.
17 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
in step 4 , steps of determining the time proportion relation of different typical load levels are as follows: step 4 . 1 : transferring a load frequency near a target load working condition to a given target load based on a principle of a consistent overall action frequency, so as to obtain a time proportion under all typical load levels; and step 4 . 2 : dynamically adjusting the time of each load working condition from the perspective of damage to meet a total damage target of the high-speed bearing in the whole life cycle load spectrum of the electric drive system.
18 . The compilation method for the reliability test load spectrum of the high-speed bearing of the electric drive system according to claim 1 , characterized in that:
in step 6 , compilation contents of the reliability test load spectrum comprise: content 6 . 1 : the reliability test load spectrum of the high-speed bearing should cover a variable amplitude loading history of the high-speed bearing under the multiple working conditions during actual operation; content 6 . 2 : in the process of compiling the reliability test load spectrum, extreme load working conditions should be considered according to a motor limit speed and a maximum torque; and content 6 . 3 : during determination of time of acceleration or deceleration in the process of transfer between load working conditions of different grades, slopes of a load rising stage and a falling stage are extracted based on an original load history, and the time when the reliability test load level rises or falls is determined based on a slope distribution model.Join the waitlist — get patent alerts
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